Modeling the Simultaneous Hydrodesulfurization and Hydrocracking

Article pubs.acs.org/EF

Modeling the Simultaneous Hydrodesulfurization and Hydrocracking of Heavy Residue Oil by using the Continuous Kinetic Lumping Approach Ignacio Elizalde* and Jorge Ancheyta Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Col. San Bartolo Atepehuacan, 07738 México D.F., México. ABSTRACT: The removal of sulfur and hydrocracking reactions that occur during hydrotreatment of heavy oil were modeled by means of the continuous kinetic lumping approach. Distillation curves of feed and products were obtained with the true boiling point method. The sulfur curve was determined from the analysis of the different fractions recovered during distillation. Sulfur was almost totally removed from the light fraction, while the heavy fraction was concentrated with this impurity. A total of eight parameters were calculated to model both reactions (five for hydrocracking and three for hydrodesulfurization). The comparison of predictions with experimental data indicates good agreement in the entire distillation and sulfur curves.

1. INTRODUCTION Hydrotreatment (HDT) of petroleum heavy residue has been subject of different studies regarding kinetics and reactor modeling and design.1,2 Various setups, reaction conditions, feed, and catalysts, as well as reactor models and kinetic approaches, are used to accurately predict/simulate pilot and industrial hydrotreatment reactor performance. Although sophisticated analyzers have been developed, the exact chemistry of hydrodesulfurization (HDS) and hydrocracking (HDC) of heavy petroleum fractions is beyond the scope of any analytical technique due to the huge amount of compounds and the complexity of the feeds and reactions. Since kinetics drives the reactor performance,3 deriving the reaction rate coefficients although apparent can help understand the reacting systems and also improve the efficiency of those reactors and of the entire commercial plant.4 Various kinetic expressions have been used in the literature for modeling HDS reactions, such as structural approach, linear free energy relationship, continuum theory, and the classical lumping.5−11 It is well-established that simpler kinetic and reactor models can be used with confidence for elemental purposes, that is, the simulation of the effects of reaction conditions on sulfur content in the liquid product in a shortrange of variation of these conditions,12 effect of volatility,13 quench location,14 and deactivation effects,15 among others. To improve the description of HDS reactor performance, other levels of complexity must be introduced such as partition of the whole lump kinetics, heterogeneous reactor model, and hydrodynamic parameters,16 although more detailed experimental data are mandatory. Other important facts that must be studied are the reaction pathways and consistent mechanisms. Historically, hydrocracking and hydrodesulfurization have been studied as separate reactions. These reactions are considered to be the most important ones during hydroprocessing of heavy crudes and bottom-of-barrel. On the one hand, various approaches to model hydrocracking have been widely discussed in the literature.17−20 On the other hand different kinetic models for hydrodesulfurization have been summarized in recent contributions.1,2 Despite the large © 2012 American Chemical Society

number of contributions reported in the literature regarding these two reactions, only a few attempts to model the simultaneous HDC and HDS are available. For instance, Verstraete et al.21 have employed the lumping discrete approach to model the hydrocracking of vacuum residue and to follow the evolution of concentration of sulfur, nitrogen, and metals in lumps as function of reactor length. Sadhighi et al.22 have modeled the hydrocracking reaction considering the hydrotreatment effect on the boundary condition of hydrocracking process, and Khorashed et al.10 have successfully simulated the distribution of sulfur in bitumen as function of continuous stirred tank reactor (CSTR) space−time. The continuous kinetic model is an acceptable approach that allows for simulating the different reactions that occur during hydrotreatment of heavy oils and residua.8,23,24 The attractiveness of this model is its accurate predictions/simulations, which can be obtained with a few parameters.8,23 Also, although the parameters are derived from experimental data, this model overcomes some of the main disadvantages of those based on total lumping such as arbitrary reaction order, inaccurate predictions of light and heavy compounds after reaction, and the need to perform extensive experimental work to calculate a number of rate constants.22 Other disadvantages of the use of discrete lumping are as follows:4 • inability to extrapolate different feedstocks as a result of the existence of different composition of the same range of boiling points • variations of composition of lumps as conversion changes and consequent variation of true kinetics • reaction mechanism that is not incorporated into kinetic scheme (few lumps) • inability to predict changes in product properties The continuous kinetic model, on the other hand, has the following advantages:8−10,23,24 Received: December 6, 2011 Revised: March 7, 2012 Published: March 8, 2012 1999

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Table 1. Complementary Equations for the Hydrocracking Continuous Kinetic Lumping Model TBP − TBP(l) TBP(h) − TBP(l)

θ=

kHDC = θ1/ α k max S0 =

∫0

K

(7)

(8)

1 {exp[ − [((x /K )a0 − 0.5)/a1]2 ] − A + B} D(x) dx 2π C(t ) =

∫k

k2

c(x , t ) D(x) dx

(10)

1

Ct (t ) = 1 N

∫0

∫0

k max

k max

c(x , t ) D(x) dx

D(x) dx = 1

• prediction of the entire boiling point curve with few model parameters • accurate following of the process chemistry • single reaction order with physical meaning • easy way to calculate any fraction with arbitrary initial and final boiling points • prediction of distribution curve of heteroatoms • easy adaptation to kinetics of heavy and extra-heavy oils and residua Although most of these advantages/disadvantages are important, the most relevant one of continuous kinetic model over discrete lumping is the possibility for predicting the evolution of heteroatom concentration as function of residence time and boiling point distribution. In this contribution, the continuous kinetic lumping model was applied to simulate simultaneously the hydrocracking and hydrodesulfurization of heavy residue oil carried out in a hydrotreatment bench-scale reactor. The reactor model was assumed to be pseudo-homogeneous, and the apparent kinetic model parameters were determined from experimental information.

(11)

(12)

In the integral function, p(kHDS, K) is defined mathematically by eq 2. p(kHDC , K ) =

+ B} A = exp( −(0.5/a1)2 )

(3)

B = δ[1 − (kHDC/K )]

(4)

Equation 2 allows for representing the yield distribution function that accounts for the amount of formation of species with reactivity kHDC from species of reactivity K (being K greater than kHDC). Other features related to p(kHDC, K) are23 (a) p(kHDC, K) is equal to zero for kHDC = K (b) p(kHDC, K) satisfies the mass balance criterion given by eq 5.

2.1. Description of Hydrocracking Model. The experimental setup has been modeled as a pseudo-homogeneous plug-flow reactor. The classical continuous kinetic model23 was used for hydrocracking reaction; thus, the mass balance into the reactor for the species with reactivity k can be represented by an integro-differential equation as

HDC

K

P(x , K ) D(x) dx = 1

(5)

(c) p(kHDC, K) is a positive function between the ranges of validity of model parameters. (d) p(kHDC, K) = 0 if kHDC > K, which means that dimerization effects are not significant. D as function of reactivity is a factor of change or Jacobian that allows for proper transforming the discrete distribution of hydrocarbons in any mixture to a continuous description.25 Mathematically, D is defined as

dc(kHDC , τ) = −kHDC·c(kHDC , τ) dτ k max

(2)

where

∫0

∫k

1 S0 2π {exp[− [((kHDC/K )a0 − 0.5)/a1]2 ] − A

2. THE MODEL

+

(9)

D(kHDC) =

p(kHDC , x) ·x ·c(x , τ) ·D(x) ·dx

N α α− 1 α kHDC k max

(6)

A list of complementary equations is given in Table 1, and the symbols are described in the Nomenclature section. The model parameters are α, a0, a1, δ, and kmax, and they must have positive values. Other restrictions such as mass conservation and normalization criterion for species type distribution function (eq 12) are met in the continuous kinetic approach. 2.2. Description of Hydrodesulfurization Model. For modeling the HDS, it was assumed that a huge amount of sulfur compounds in reactant mixture is present. A relationship

(1)

This equation describes the fact that the variation of any species (c(kHDC, τ)) as function of residence time (τ) and hydrocracking reactivity (kHDC) depends on two factors: (1) the rate of hydrocracking of such a compound (first term of right-hand side) and (2) its production from larger molecules, that is, higher boiling point compounds (second term of righthand side) 2000

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between dimensionless true boiling point temperature and sulfur compound reactivity has been derived by Sau et al.:8 kHDS = k minS − k maxS ln[e−1 − (e−1 − 1)θ1/ β]

which means that the variation of concentration of any sulfur compound as function of residence time is due to two facts: (1) diminution of any sulfur compound content (first term of the right-hand side, kHDS) by hydrogenolysis activity of the catalyst (HDS) and the hydrocracking of that compound into smaller boiling point sulfur species and (2) simultaneous production of sulfur by the hydrocracking reaction of larger molecular weight fractions (second term of the right-hand side, kHDC). It is observed that this term is similar to that of hydrocracking, but instead of using c(kHDS,t), that is, the hydrocarbons with higher boiling points, it is necessary to use cS, the sulfur concentration on those hydrocarbons. One should note that kHDC and kHDS are both function of dimensionless temperature. So that for any HDS reactivity compound, there is an HDC reactivity, and they can be related each other by means of eqs 8 and 13, although interpolation may be needed. The model parameters for HDS apart from those of hydrocracking are β, kmaxS and kminS. kmaxS is the HDS reactivity of the lowest possible boiling point compound containing sulfur, whereas kminS is the reactivity of the highest boiling point compound bearing-sulfur atoms. From eq 17, if kmax tends to zero, such an expression is reduced to eq 15; that is, HDS is independent of HDC because the distribution of boiling point of the feed remains without changes with respect to the product. 2.3. Solution of Model. Sulfur distribution and hydrocarbon concentration in the feed can be found from the solution of eqs 1 and 17 by using a similar procedure as that reported elsewhere.26 First, eq 1 was solved to find the hydrocracking kinetic model parameters: α, a0, a1, δ, and kmax. Then, by using these values, eq 17 was resolved, and the parameters β, kmaxS, and kminS were found. All routines were written in MatLab software. The criterion of minimization of the sum of square errors (SSE) obtained from the difference between calculated and experimental points was employed to determine all model parameters. More details of the numerical solution of eq 1 can be found elsewhere.26

(13)

Such a relationship was obtained from experimental information of model compounds, and it is basically an expression with adjustable parameters.8 Equation 13 indicates that the reactivity of sulfur compounds decreases monotonically as true boiling point of fraction increases; that is, light fractions contain the most reactive sulfur compounds, while heavy fractions are concentrated with the most refractory sulfur compounds.8 The number of sulfur compounds in the petroleum mixture is finite but unknown; in spite of this, the continuous kinetic approach allows for continuous description of this property. The kinetic behavior of each sulfur compound must remain invariant, even if its distribution is described as a continuum function; so that in order to keep the consistence between discrete and continuous descriptions, a factor must be introduced. The factor or Jacobian to change from θ to k coordinates was assumed to be8 D(kHDS) = N

dθ dkHDS

(14)

The derivative of θ, with respect to the HDS reactivity coefficient, can be easily obtained from eq 13. If only the HDS reactions of different sulfur compounds are considered to take place, the differential mass balance for each compound in a plug-flow reactor assuming power-law kinetics can be written as dcS = −kHDScS (15) dτ According to previous reports, the reaction order has been considered to be 1.7 The total concentration of sulfur in liquid can be calculated in a similar manner as that for hydrocracking (eq 11); that is, wtStotal(τ) =

∫k

k maxS minS

cS(kHDS , τ) D(kHDS) dkHDS

3. EXPERIMENTAL SECTION

(16)

An atmospheric residue from a heavy crude oil of 13° API was used as feedstock for hydrotreatment experiments. The main properties of the residue feed are as follows: 5.4° API, 5.74 wt % sulfur, 722 ppm Ni + V, and 21.77 wt % insolubles in C7. The feed passes through two catalytic bed bench-scale reactors in series packed with Ni−Mo supported over alumina hydrotreatment catalyst, properties of which are reported in Table 2. The test was conducted at total liquid−hourly space−velocity of 0.2 h−1, reaction temperature of 382 °C, total

One can observe that D(kHDS) plays the role of weight factor in the integral of eq 16 similar to D(kHDC) for hydrocracking in eq 11. In the HDT reactor, simultaneous hydrocracking and hydrodesulfurization occurs; that is, the hydrodesulfurization reaction proceeds considering parallel reactions of HDC and HDS,10 as observed in Figure 1. Hence, the material balance,

Table 2. Physical and Chemical Properties of Catalyst nominal size, inch Ni, wt % Mo, wt % surface specific area, m2/g pore vol., mL/g pores size distribution, vol % 1000 Å

Figure 1. Conversion of sulfur compounds via HDS and HDC.10

following the pathways shown in such a figure, can be written, instead of eq 15, as k max dcS = −(kHDS + kHDC)cS + p(k , x ) dτ k

∫

xcS D(x) dx

(17) 2001

1 /18 1.12 4.36 205.3 0.825

12.2 24.22 48.50 12.69 1.73 0.66

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pressure of 9.6 MPa, and hydrogen-to-oil ratio of 5800 SCF H2/bbl oil. The feed and products were characterized in order to determine the total sulfur content and distillation curve. Sulfur content in feedstock and products was determined with HORIBA equipment (SLFA-2100) by using the ASTM D-4294 standard method. The variation coefficient of the analysis with this instrument is 0.006%. The distillation curve was found using the True Boiling Point (TBP) method. During distillation, it was possible to recover different fractions, which were further analyzed by sulfur content, so that, apart from the distillation curve, the sulfur curve was also generated.

4. RESULT AND DISCUSSION 4.1. Hydrocracking Reaction. The experimental data of the distillation curves (i.e. boiling temperature versus weight percent) were used, together with eq 1, to determine the model parameters for hydrocracking. The values of the five parameters are α = 0.35, a0 = 1.50, a1 = 22.0, δ = 1.31 × 10−8, and kmax = 0.18 h−1. The value of kmax is a direct indicator of the hydrocracking extent, from which it is deduced that this reaction proceeds at low rate, because of the operation at moderate conditions. The comparison of simulated and experimental distillation curve data for the feed and the hydrotreated product is shown in Figure 2. Good agreement is

Figure 3. Comparison of experimental data (symbols) of hydrodesulfurization and simulated results (lines). (●) Feedstock sulfur distribution, (○) product sulfur distribution. T = 382 °C, P = 9.8 MPa, LHSV = 0.2 h−1, and H2-to-oil ratio = 5800 SCF/bbl.

parity plot of 1.003 and 1 × 10−4, respectively, and square correlation coefficient of 0.9996. It is interesting to note that the molecular weight and complexity of the sulfur compounds present in the heavy feed increase as the boiling point also increases. Also, their reactivity decreases in general with the heaviness of the fraction; the hardest-to-react sulfur compounds are those that have the sulfur atom surrounded by alkyl groups, such as 4−6 dimethyl dibenzothiophene. In spite of all these particular characteristics of the sulfur curve, the continuous kinetic lumping approach used here captures in a precise manner the different reactivities and can properly simulate both the hydrocracking and the hydrodesulfurization reactions. Regarding the shapes of the sulfur curves of the feed and the hydrotreated product, they are typical ascending curves, which indicate that the heavier the fraction the more sulfur content that they contain. From the sulfur curve of the product it is observed that sulfur in light fractions is almost totally removed, while in the heavy fraction (i.e. vacuum residue), sulfur content, although drastically reduced, is still present. In the heavy fraction, the reduction of sulfur content can be attributed essentially to proceed via hydrocracking because the sulfur compounds that this fraction possesses are harder-to-react, that is, refractory in nature, under the operating conditions studied, which is corroborated by the low value of kminS. It is therefore confirmed that removal of sulfur-bearing compounds is linked to hydrocracking, and the influence of HDC reaction on HDS reaction should be taken into account for kinetic studies. From these results, it is concluded that by using the continuous kinetic lumping model one is capable to predict the yield of a particular distillate and its sulfur distribution under typical reaction conditions. 4.3. Final Considerations. A few attempts have appeared in the literature to try to model the hydrodesulfurization together with hydrocracking reactions. Some of those approaches omit the fact that the reactions proceed simultaneously. This assumption is valid only if no appreciable extent of hydrocracking takes places during hydrotreatment,11 which typically occurs during processing of distillates, for example, naphtha, gas oil, or even fluid catalytic cracking feed (vacuum gas oils), but not when hydrotreatment of heavy feeds. A typical parameter employed in correlations for transport properties of petroleum fractions is the average boiling point that is assumed to be constant. This is true only if no appreciable extent of hydrocracking occurs, but if there is any,

Figure 2. Comparison of experimental data (symbols) of hydrocracking and simulated results (lines). (●) Feedstock, (○) hydrocracked product. T = 382 °C, P = 9.8 MPa, LHSV = 0.2 h−1, and H2to-oil ratio = 5800 SCF/bbl.

observed, and global absolute error was less than 2%. It is also seen that hydrocracking selectivity toward middle distillates is more favored than that of lighter fractions, which undergoes almost no HDC reaction. In other words, at the reaction conditions of the present study, the severity is such that heavy fractions are converted to light fractions in a cascade mechanism (i.e. vacuum residue to vacuum gas oil, vacuum gas oil to middle distillates, and so forth), but it is not sufficient to increase the yield of the lightest fraction, such as naphtha. 4.2. Hydrodesulfurization Reaction. The experimental data of the sulfur curves (i.e. boiling temperature versus sulfur content) was used, together with eq 17 and the values of parameters of the hydrocracking model previously determined, to calculate the model parameters for the hydrodesulfurization reaction, which resulted to be kmaxS = 7.5 h−1, kminS = 0.08 h−1, and β = 2. The comparison of simulated and experimental sulfur curves is shown in Figure 3. Similarly to hydrocracking reaction, good agreement is also observed for HDS reaction with global absolute error less than 2%. Other statistical parameters also confirm the good correspondence between experimental and simulated results: slope and intercept from 2002

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C(τ) = concentration in weight fraction of any pseudocomponent with arbitrary boiling point range as function of residence time. C′(τ) = total concentration in weight fraction of hydrocarbon as function of residence time. cS = sulfur concentration of the component with reactivity kHDS at any residence time. D(kHDC) = species-type distribution function for hydrocracking reaction. D(kHDS) = species-type distribution function for hydrodesulfurization reaction. e = exponential function basis. k, kHDC = hydrocracking reactivity of any species (h−1). kHDS = hydrodesulfurization reactivity of any species (h−1). kmax = hydrocracking reactivity of the species with the highest TBP in the mixture (h−1). kmaxS = hydrodesulfurization reactivity of the species with the lowest TBP in the mixture (h−1). kminS = hydrodesulfurization reactivity of the species with the highest TBP in the mixture (h−1). N = total number of species in the mixture. TBP = true boiling point of any pseudocomponent (K). TBP(h) = highest boiling point of any pseudocomponent in the mixture (K). TBP(l) = lowest boiling point of any pseudocomponent in the mixture (K). x = hydrocracking reactivity of any species (h−1); variable of integration. wt = weight fraction of species.

changes in transport properties can occur and the reactor model can fail under these circumstances. This fact, if not properly taken into consideration, can lead to additional model parameters as factors that mask the fundamental behavior of the HDT reactor. If the total sulfur curve is simulated by using any model that considers total lumping or averaging any profile distribution without proper validation with experimental data, prediction of sulfur in products can be restricted to short-range of reaction conditions and reliable results cannot be expected. If a sulfur distribution is assumed by taking from the literature any correlation between sulfur content and boiling point, the use of the experimental sulfur curve data to validate/derivate the model parameters is mandatory.25 Having reliable data of distillation and sulfur curves is not an easy task. The TBP method requires at least four liters of sample to perform the distillation and simultaneously recover different fractions for further sulfur and API gravity analyses. If more detailed analysis is required, the TBP method indicates the use of forty liters of sample. Obtaining this amount of sample is another problem to face. Typically, experiments are carried out in small setups, which use low feed flow rate, and this requires long time to collect the needed quantity of HDT product. These are the main reasons why research groups working on hydroprocessing of heavy oils do not perform studies such as the one developed in this investigation. Other authors have reported the application of continuous kinetic lumping to model HDS and changes in product properties; however, neither the assumptions nor the validation with suitable experimental data have been properly reported and discussed.

Greek Letters

■

CONCLUSION The simultaneous hydrocracking and hydrodesulfurization reactions were modeled by using the continuous kinetic lumping approach. Five parameters were obtained for the hydrocracking reaction while three parameters were obtained for hydrodesulfurization. Despite the different reactivity of all types of sulfur compounds contained in the heavy oil, both reactions (HDS and HDC) were properly represented by the continuous kinetic lumping approach. Good agreement between experimental and predicted distillation and sulfur curves was obtained.

■

■

α = model parameter of eq 6. β = model parameters of eq 13. δ = model parameter of hydrocracking yield distribution function (p(k, K)). θ = normalized TBP as defined in eq 7, dimensionless. τ = inverse of space velocity or residence time (h).

REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: +52 55 9175 8418. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I. Elizalde thanks Instituto Mexicano del Petróleo for financial support during his postdoctoral fellowship.

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NOMENCLATURE a0, a1, S0 = parameters of yield distribution function eq 2. c(k, τ) = concentration of the species with reactivity k at residence time τ. c(k, 0) = concentration of the species with reactivity k in the feed. 2003

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